We present the results of efficiency and power output for irreversible Carnot-like heat engines with nonlinear inverse, Dulong-Petit and Stefan-Boltzmann heat transfer laws when optimized with a recent criterion. A unified working regime is found intermediate between those predicted by the maximum efficiency and maximum power for all realistic values of the parameters accounting for the irreversibilities: finite rate heat transfer between the working fluid and the external heat sources, internal dissipation in the working fluid, and heat leak between reservoirs.